DAY 424

ODDLY ADDICTIVE
Credit: GAMES Magazine - March, 2008
Burt Hochberg

Assume that the two sets of figures below are correctly aligned. Which set would you think adds up to the higher total?

987654321     123456789
  87654321     12345678
    7654321     1234567
      654321     123456
        54321     12345
          4321     1234
            321     123
              21     12
________1     1___________

Answer:

Both columns of numbers add up to the same total: 1,083,676,269. The zeros omitted from the numbers on the right are implied by the alignment of the column.

Explanation (by Philip Sakievich):  Notice the 1's in the set to the right. There are nine of them, each in the hundred-millions column. They total to nine hundred million. This corresponds to to the 9 in the first number at the top of the set to the left, which is also in the hundred millions column. There are eight 2's in the set to the right, each in the ten millions column. Each 2 stands for twenty million. Together they total to 160 million. This corresponds to the two 8's in the set to the left, each also in the ten millions column. Each 8 stands for eighty million, for a total of 160 million. The seven 3's to to the right total 21 million, corresponding to the three 7's on the left which also total to 21 million. And so on until the 9 in the ones column at the end of the set to the right, corresponding with the nine 1's in the ones column of the set to the left.